Some extensions to digital signal processing.

Some practical extensions to digital signal processing techniques are presented. Firstly, an account is given of a curve-fitting procedure designed to give a detailed analysis of time functions, either wholly or in part dominated by a single sinewave, such as an amplitude or frequency-modulated carrier. The remainder, and large majority, of the thesis is devoted to the discrete Fourier transform (D.F.T.) and power spectral estimation. Two binary transforms, the Walsh and the new Intermediate Binary Transform, are related theoretically to the D.F.T. to give practical computational procedures, which prove to be more flexible than the 'fast' Fourier transform and more efficient for short length data sequences. Approximations in the calculations leading to power spectral estimates are proposed and examined. In particular, round-off to the nearest integer power of two is applied to the transform coefficients of the D.F.T. procedures. An important principle here is the phase invariance property which permits harmonics to be normalised individually, and the errors to be viewed purely in terms of harmonic leakage. An isometric plotting routine is used to provide a convenient form of display for functions of three variables, and examples are given of both time-varying power spectra of a single channel electroencephalogram recording and the harmonic leakage due to the said round-off